The inverse problem of a Gaussian convolution and its application to the finite size of the measurement chambers/detectors in photon and proton dosimetry.

Abstract:

:A Gaussian convolution kernel K is deduced as a Green's function of a Lie operator series. The deconvolution of a Gaussian kernel is developed by the inverse Green's function K(-1). A practical application is the deconvolution of measured profiles Dm(x) of photons and protons with finite detector size to determine the profiles Dp(x) of point-detectors or Monte Carlo Bragg curves of protons. The presented algorithms work if Dm(x) is either an analytical function or only given in a numerical form. Some approximation methods of the deconvolution are compared (differential operator expansion to analytical adaptations of 2 x 2 cm2 and 4 x 4 cm2 profiles, Hermite expansions to measured 6 x 6 cm2 and 20 x 20 cm2 profiles and Bragg curves of 80/180 MeV protons, FFT to an analytical 4 x 4 cm2 profile). The inverse problem may imply ill-posed problems, and, in particular, the use of FFT may be susceptible to them.

journal_name

Phys Med Biol

authors

Ulmer W,Kaissl W

doi

10.1088/0031-9155/48/6/302

subject

Has Abstract

pub_date

2003-03-21 00:00:00

pages

707-27

issue

6

eissn

0031-9155

issn

1361-6560

journal_volume

48

pub_type

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